Spherical mean periodic functions on semisimple Lie groups

Spherical spectral synthesis and two-radius theorems on Damek–Ricci spaces

“…Theorem 1.4 below carries over this result to radial functions in Damek-Ricci spaces. For symmetric spaces of rank one, spherical spectral synthesis was proved in [3]. For further results on spectral synthesis in symmetric spaces see, e.g., [4], [5] and [21].…”

Spectral analysis for radial sections of some homogeneous vector bundles on certain noncompact Riemannian symmetric spaces

“…For even functions on R we have the following version of this theorem (see [2]): For λ ∈ C, let ψ λ (x) = (e iλx + e −iλx )/2.…”

“…On the other hand, the theorem is extended for the group SL(2, R) by Ehrenpreis and Mautner [16] and for K-biinvariant functions of rank one symmetric spaces by Bagchi and Sitaram [2].…”

An analog of the Schwartz theorem on spectral analysis on a hyperbolic plane

“…Some analogs of the theorem by L. Brown, B. M. Schreiber, and B. A. Taylor for noncompact symmetric spaces X = G/K of rank 1 (see, e.g., [12]) were considered in works [10,11]. There, it was shown that any nonzero subspace U in C(X) that is invariant relative to the group G contains a spherical function…”